Orthogonal frequency division multiplexing (OFDM)-based integrated sensing and communication (ISAC) is promising for future sixth-generation mobile communication systems. Existing works focus on the joint estimation of the targets' range and velocity for OFDM-based ISAC systems. In contrast, this paper studies the three-dimensional joint estimation (3DJE) of range, velocity, and azimuth for OFDM-based ISAC systems with multiple receive antennas. First, we establish the signal model and derive the Cramer-Rao bounds (CRBs) on the 3DJE. Furthermore, an auto-paired super-resolution 3DJE algorithm is proposed by exploiting the reconstructed observation sub-signal's translational invariance property in the time, frequency, and space domains. Finally, with the 5G New Radio parameter setup, simulation results show that the proposed algorithm achieves better estimation performance and its root mean square error is closer to the root of CRBs than existing methods.